scholarly journals A note on the orderability of Dehn fillings of the manifold v2503

2020 ◽  
Vol 29 (11) ◽  
pp. 2071002
Author(s):  
Konstantinos Varvarezos
Keyword(s):  
Dehn Filling ◽  
Dehn Fillings

We show that Dehn filling on the manifold [Formula: see text] results in a non-orderable space for all rational slopes in the interval [Formula: see text]. This is consistent with the L-space conjecture, which predicts that all fillings will result in a non-orderable space for this manifold.

scholarly journals EXAMPLES OF REDUCIBLE AND FINITE DEHN FILLINGS

2010 ◽  
Vol 19 (05) ◽  
pp. 677-694 ◽  
Author(s):  
SUNGMO KANG
Keyword(s):  
Hyperbolic Manifolds ◽  
Dehn Filling ◽  
Dehn Fillings

If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperbolic manifolds admitting a reducible Dehn filling and a finite Dehn filling of every type: cyclic, dihedral, tetrahedral, octahedral and icosahedral.

Connect sum of lens spaces surgeries: application to Hin recombination

2011 ◽  
Vol 150 (3) ◽  
pp. 505-525 ◽  
Author(s):  
DOROTHY BUCK ◽  
MAURO MAURICIO
Keyword(s):  
Lens Space ◽  
Lens Spaces ◽  
Branched Covers ◽  
Dehn Filling ◽  
Connected Sum ◽  
Hin Recombinase ◽  
Complete Set ◽  
Dehn Fillings ◽  
Filling Problem ◽  
Tangle Model

AbstractWe extend the tangle model, originally developed by Ernst and Sumners [18], to include composite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by studying the corresponding Dehn filling problem via double branched covers. In particular, we build on results on exceptional Dehn fillings at maximal distance to show that if Dehn filling on an irreducible manifold gives a lens space and then a connect sum of lens spaces, the distance between the slopes must be one. We then apply our results to the action of the Hin recombinase on mutated sites. In particular, after solving the tangle equations for processive recombination, we use our work to give a complete set of solutions to the tangle equations modelling distributive recombination.

AN EXAMPLE OF A HYPERBOLIC 3-MANIFOLD REALIZING A BOUND ON DEHN FILLINGS

2006 ◽  
Vol 15 (03) ◽  
pp. 299-311
Author(s):  
LORENA ARMAS-SANABRIA
Keyword(s):  
Intersection Number ◽  
Dehn Filling ◽  
The Core ◽  
Longitudinal Slope ◽  
Genus 2 ◽  
Dehn Fillings

Let M be a compact, orientable, irreducible 3-manifold with an incompressible torus boundary T and γ a longitudinal slope on T, which bounds a surface F of genus 2. Suppose there exists a slope r that produces an essential 2-sphere S by Dehn filling. Let q be the minimal geometric intersection number between the essential 2-sphere and the core of the Dehn filling. Matignon and Sayari [5] proved that either q = 2 or the minimal geometric intersection number between γ and r is bounded by 3. Here, we construct an example of a hyperbolic 3-manifold realizing that bound.

ESSENTIAL LAMINATIONS, EXCEPTIONAL SEIFERT-FIBERED SPACES, AND DEHN FILLING

1998 ◽  
Vol 07 (04) ◽  
pp. 425-432 ◽  
Author(s):  
MARK BRITTENHAM
Keyword(s):  
Recent Work ◽  
Dehn Filling ◽  
Manifold With Boundary ◽  
Seifert Fibered Spaces ◽  
Dehn Fillings

We show how essential laminations can be used to provide an improvement on (some of) the results of the 2π-Theorem; at most 20 Dehn fillings on a hyperbolic 3-manifold with boundary a torus T can yield a reducible manifold, finite π1 manifold, or exceptional Seifert-fibered space. Recent work of Wu allows us to add toroidal manifolds to this list, as well.

scholarly journals Farrell–Jones via Dehn fillings

2018 ◽  
Vol 10 (04) ◽  
pp. 873-895 ◽  
Author(s):  
Yago Antolín ◽  
Rémi Coulon ◽  
Giovanni Gandini
Keyword(s):  
Free Product ◽  
Infinite Order ◽  
Dehn Filling ◽  
Residually Finite ◽  
Finite Subgroups ◽  
Dehn Fillings

Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order subgroups have a certain structure of a free product. We then apply this result to establish the Farrell–Jones conjecture for groups hyperbolic relative to a family of residually finite subgroups satisfying the Farrell–Jones conjecture, partially recovering a result of Bartels.

scholarly journals Explicit Dehn filling and Heegaard splittings

2013 ◽  
Vol 21 (3) ◽  
pp. 625-650 ◽  
Author(s):  
David Futer ◽  
Jessica S. Purcell
Keyword(s):  
Heegaard Splittings ◽  
Dehn Filling

Reducing Spheres and Klein Bottles after Dehn Fillings

2003 ◽  
Vol 46 (2) ◽  
pp. 265-267 ◽  
Author(s):  
Seungsang Oh
Keyword(s):  
Short Proof ◽  
Klein Bottle ◽  
Dehn Fillings

AbstractLet M be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on M along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.

scholarly journals Boundaries of Dehn fillings

2019 ◽  
Vol 23 (6) ◽  
pp. 2929-3002 ◽  
Author(s):  
Daniel Groves ◽  
Jason Fox Manning ◽  
Alessandro Sisto
Keyword(s):  
Dehn Fillings

A Note on Finite Dehn Fillings

1999 ◽  
Vol 42 (2) ◽  
pp. 149-154
Author(s):  
S. Boyer ◽  
X. Zhang
Keyword(s):  
Finite Volume ◽  
Hyperbolic Metric ◽  
Fundamental Groups ◽  
Dehn Fillings ◽  
Zero Class

AbstractLet M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in H1(∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.

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